Rewrite as a simplified fraction. ${2.51\overline{5} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 2515.5555...\\ 100x &= 251.5555...\end{align*}}$ Subtracting the two equations, we have: ${900x = 2264}$ ${x = \dfrac{2264}{900}} $ ${x = \dfrac{566}{225}} \text{or} {2 \dfrac{116}{225}}$